Question

How does the volume of a cylinder change when it’s diameter is doubled

Answer 1

Recallin that, the diameter is twice as long as the radius, namely the radius is half the diameter, so, if the diameter is doubled, the radius is also doubled.

$\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h\quad \begin{cases} r=radius\\ h=height\\ -----\\ r=\stackrel{doubled}{2r} \end{cases}\implies V=\pi (2r)^2 h \\\\\\ V=\pi (2^2r^2)h\implies V=\pi 4r^2 h\implies V=4~(\pi r^2 h)$

notice, the new volume is 4 times (πr² h), namely 4 times the original.